Use the "Edit This Page" button and place your brief description of how you see yourself excitedly moving forward.
More specifically:
How do you want to be involved in the project? (level of involvement)
Given the "framework" write a paragraph explaining a study that could be located in the framework
other studies or proposals you have that may be relevant
Include your NAME
Glenda Lappan
In a specific area of mathematics (rational numbers or algebra), what happens to the mathematics as it is transformed through the four stages of the framework?
Sandra Crespo
I like Glenda's question at the preservice setting;
what happens to a particular math idea as it moves through the sequence of written, enacted, and learned curriculum inside a teacher preparation program --- within math content courses and within math methods courses.
Sandra Crespo
(again)
I am currently working on my CAREER project that I see has connections to this group
1. Study of preservice teachers' development of practices of posing, interpreting, and responding
As part of this study we have looked at the opportunities to learn that pteachers in MSU program have had to learn these three practices in the math for teaching and math methods courses. We have looked at the written curriculum for clues into what about these practices one might expect preservice teachers to learn in our program.
As part of this collective --- I can imagine a project that does a more fine grained analysis of opportunities to learn of a particular math idea and practice (say algebraic thinking and how to pose tasks within that strand). Jeffrey Choppin Level of involvement
For the next 2 years, I cannot commit substantial time to any new projects. I am just beginning a 5-year CAREER grant (described in more detail below) and am 2 years from submitting my tenure package, so I will need to spend most of my time in the immediate future writing from my current study.
Description of CAREER grant - Adapting Curriculum for Learning in Mathematics Education (ACCLIME)
I will describe the ways my CAREER grant fits into the framework put forth by the group today. The CAREER grant focuses on mostly experienced CMP teachers who have received considerable CMP-specific professional development and who teach in districts that have used CMP as the primary curriculum resource for 5 or more years.
The study focuses on teacher knowledge of the ways that CMP units engage students with mathematical content. I use a unit as the level of analysis in order to get at teachers’ understanding of how ideas develop over the unit. For a subset of teachers, I have longitudinal data that look at successive enactments of the same unit over 2 or 3 years to see how their adaptations reflect teacher knowledge of student thinking and teacher learning with respect to how the CMP materials engage students. I have also studied the policy context around the adoption and implementation of CMP to provide background for the ways that the teachers use CMP.
The ways that I see that my study contributing to the set of studies is that it looks at teacher learning through enacting curricula. I can also connect teacher learning, and curricular orientations, to teachers’ practices that contribute to maintaining cognitive complexity, which I characterize as teaching for understanding. My data and analysis can speak directly to the framework, though with the major limitation that I do not focus on student learning. Jon Davis My Interest
I am interested in the maintenance of high cognitive demand of tasks across the written, intended, and enacted curriculum and its connection to student learning. If I was to zoom in on one component of that slice it would be the implementation of high cognitive demand tasks in the enacted curriculum and the roles that the curriculum plays in preparing high school mathematics teachers for that enactment in addition to the learning that may or may not occur by teachers in this area as they enact these tasks.
My Role
I am interested in being a co-PI on a project and working on the proposal. While I won’t be there physically to write the proposal as part of a group I am interested in contributing from a distance by taking turns developing a draft.
Recent Proposal
I recently submitted an NSF REESE proposal with Jeff Shih at the University of Nevada – Las Vegas and Rich Brown at USC. The intent of that proposal is to develop valid and reliable measures of specialized content knowledge (SCK), knowledge of content and students (KCS), and knowledge of content and teachers (KCT) in introductory high school algebra. We also intend to gather large-scale information on how teachers read, evaluate and adapt three NSF-funded and three commercially developed high school curricula as well as the nature of the enacted curriculum within these different programs. During year three of the project we are looking for connections between teachers’ use of curricular resources, the enacted curriculum, and growth in SCK, KCS, and KCT. Kristen Bieda
I am interested in devoting a significant chunk of time to a project related to this work, in a co-PI capacity.
I would like to propose a study around the question of: In what ways are teachers' conceptions of the coherency among "big ideas" or concepts in a unit or a succession of units influenced by the curriculum in its various stages of implementation? I am particularly interested what happens with teachers' conceptions of the coherency as the lesson or unit is enacted. This study fits into the framework proposed by the group as the purposes of engaging students in cognitively demanding tasks is only relevant for teachers if they recognize how the content is part of a bigger, coherent "whole." Additionally, teachers' ability to situate content from a task to the mathematical goals for a unit is a part of mathematical knowledge for teaching.
I am also interested in examining mentor/intern interactions around K-12 curriculum. While PSTs' experiences in methods courses may support their emerging practices in enacting tasks from the K-12 curriculum at a high level, their mentor teachers may or may not "sanction" (for lack of a better word) these practices. Another way of studying these interactions would be to look at how mentor teachers' and PSTs' conceptions of the mathematics in the curriculum evolve during these interactions. Janine Remillard My Interests
I find all of components of the research framework interesting, however, with respect to what I would like to actually take on, I can imagine two, related areas of work. First, I am interesting in analyzing curriculum materials with an eye toward developing clearer and more precise ways of describing and categorizing them. I am particularly interested in developing a set of dimensions of curriculum materials that might be used classify them (that move us beyond categories like reform and traditional). Some of these dimensions (as described in others’ research) fit into the broad categories of a) mathematical stance (underlying assumptions about what it means to learn mathematics, how the content is organized, nature of tasks or cognitive demand), b) pedagogical stance, including the uses of formative assessments c) support for teacher use (how the resource communicates with the teacher). Second, I am interested in examining how teachers interact with the materials—specifically the components described above. I’m curious about how and what teachers read, the process by which the “intended curriculum” is designed, and the various factors (individual, contextual, curricular) that influence it.
Level of Involvement
I imagine myself being substantially involved in both these lines of inquiry as a PI/CoPI or as one of the senior personnel. This includes working on the proposal.
Other Research on the Burner
I am currently working on a proposal with Ok-Kyeong Kim at WMU that will be submitted to DRK-12 in January. This study is an exploratory study seeking to conceptualize and develop instruments to measure pedagogical design capacity. If funded, the project would involve three years of work. Mary Kay Stein Level of Involvement
I am interested in being involved at the level of PI/Co-PI.
Ideas for a Study
I would be most interested in designing a study that examines how context (school/district characteristics and interaction patterns) and curricular features shape teacher learning. I could imagine being paired with someone who is undertaking a close-up examination of curricular materials and how teachers use them; I could design a complementary focus on how those same teachers interact with others (peers, coaches, principals) around the curriculum and to what end. Resources permitting, it would be useful to also trace the between-community boundary practices that shape and are shaped by the curriculum.
Prior Related Work
I had an IERI grant that examined the scale up Everyday Mathematics and Investigations in two districts. Michelle Cirillo
Corey Drake and I have been working on expanding her ideas about curriculum vision (first addressed by Drake & Sherin in Remillard, Herbel-Eisenmann, & Lloyd (in press)). Corey, Beth, and I wrote a series of questions designed to
help teachers develop and then enact their curriculum vision. These questions explicitly ask teachers to consider factors that influence their curriculum enactment such as national and state standards, their beliefs about the
balance of procedural fluency and conceptual understanding, the curriculum vision of their curriculum materials, and so forth.
We are interested in testing out the hypothesis that asking a teacher to explicitly think about and use his/her curriculum vision would have a positive impact on student learning. Corey and I are interested in being co-PIs (with others invited to join) on this work. We would be interested in testing this idea out in PD (and follow-up) with teachers who are enacting a new set of curriculum materials next fall (one site already identified) as well as in
districts that have already been using their materials.
We see this as fitting into the framework through comparisons of enacted
curriculum (where the written curriculum is constant for participating
teachers). We could see investigating this transformation through a particular
content focus, such as rational number. Raven McCrory
For the last 3 years, I have been doing a study of undergraduate classes for elementary teachers. The study, called ME.ET (the Mathematical Education of Elementary Teachers) has aimed to understand what mathematics is being taught, by whom, with what resources, and with what results. We have a lot of data and are now analyzing it, with some interesting outcomes. For more information about the project, see the Web site, http://meet.educ.msu.edu.
Ideas for Studies
I would like to extend the work of the ME.ET project to a larger, random sample study of mathematics classes for elementary teachers to test hypotheses about achievement in math classes. Use LMT items in post-test (no pretest). Include measures of beliefs. Instructor survey based on ME.ET, with many fewer items.
Hypotheses:
Textbook matters.
Teacher understanding matters.
Students' SAT/ACT matters (prior knowledge).
Control instructor has over class matters.
ADD: attention to and use of K-12 curricula
Study of methods classes for elementary teachers. Could select methods classes at the same schools as the above random study, thus giving a better picture of learning across the program.
Textbook, Use of curriculum materials, content and format of classes, instructors, learning goals, learning.
Same format as ME.ET: Pre/Post test in selected states, multiple institutions. Whole class testing, instructor survey.
Nesrin Cengiz
My Interest
I am interested in the implementation of high-level tasks in grades K-8.
Particularly, I'd like to explore the relationship between the support provided
in the teacher guide materials and the ways in which teachers maintain the
cognitive demand of the high-level tasks during curriculum enactment. Some of
the questions that I have in mind are:
What is the nature of the support provided in the curriculum materials to
specifically help teachers maintain the level of the cognitive demand of the
tasks during curriculum enactment?
How do teachers read and interpret that kind of information? How do they
use that kind of information during the implementation of the tasks?
What is the knowledge that teachers need to have in order to be able
read, interpret, and use the support provided in the curriculum materials in a
way that allows them to maintain the cognitive level of the tasks?
Level of Involvement
I am certainly interested in being involved in writing a proposal. As a junior
faculty, though, I feel like I need to know more about possible options for the
level of involvement. Jill Newton
Involvement: I would be interested in collaborating on a grant with faculty
interested in similar/related research questions.
Possible questions of interest:
• In what ways are curricula (K-12 curriculum materials) being used in
teacher education programs? What is the payoff for these practices?
• What are the components (curriculum?) of current secondary mathematics
methods courses? What is the overall structure of secondary mathematics
teacher education programs (What courses? In what sequence? What field
experiences?)?
• How can/do inservice teachers implement standards-based practices/tasks in
schools where a more traditional text has been adopted? Sarah Sword
I'm wondering about what it means for a teacher to have a robust enough
understanding of the mathematics of a particular curriculum to be able to make
informed decisions about implementation - how to use student (and teacher
support) materials effectively, even as the context around the teacher (and the
curriculum) varies. Sharon Senk
I have been working on several projects in recent years that have developed
instruments to assess knowledge for teaching mathematics. The samples include
local MSU students as well as international samples. In a new study, I would
like to use these instruments (and modifications of them and others that might
be available) to investigate the nature and growth of knowledge for teaching
mathematics and factors that contribute it. Specifically, I would like to study
the following:
1. additional work on construct and instrument development
2. effects of mathematics courses for future elementary teachers and methods
courses on knowledge for teaching mathematics
Ideally, I would like to make this a longitudinal study that follows a group
from several universities into the first few years of teaching.
I am also very interested an experienced in fine grained analysis of
curriculum, especially algebra, geometry, reasoning and proof in K-16
mathematics.
Jack Smith Level of involvement
I am fully booked on a current project and therefore have been cautious to do more with ExCITE than to help support the directions set by others. I cannot be directly involved, though I am interested in seeing the proposal that emerges and to see where there are connections to and potential synergies my current work (see below).
My take or slice of the proposed direction
In general, I am interested in the nature and dynamics of enactments of written curricula, of all types-especially for problematic content like fractions/rational numbers, algebra, and measurement.
Current proposed projects
The project that I just sent to NSF-REESE is a continuation of the my current STEM project which is examining the spatial measurement (length, area, and volume) content of three elementary mathematics curricula (as written)-Everyday Mathematics, Scott-Foresman/Addison-Wesley's Mathematics, and Saxon Mathematics-for their capacity to support robust student learning. In particular, we are looking for and coding each and every element of conceptual, procedural, and conventional knowledge related to measurement in each curricula. The objective is very detailed (and different sort of) opportunity to learn analysis. (We initially proposed carrying this examination through the middle grades (6-8) but the work on the elementary programs has been slower than I expected; we have not gotten to middle school yet.)
The proposed project will complete the analysis of written curricula; carry out discussions with the curriculum authors in the hopes that we can make our sense of important deficits clear and compelling (all have indicated interest in meeting with us); develop PD/summer institutes for practicing teachers and a "unit" in the mathematics methods course here at MSU for pre-service teachers that focus on (a) measurement lessons in written curricula, and (b) key conceptual content like unit iteration; and finally initiate a 'measurement mini-Center" of the major national research teams that will meet regularly to discuss and integrate their findings to get more "bang" for the national (mostly NSF) buck.
Sam Otten (just a grad student) Level of involvement
I would be interested in serving as a graduate assistant for a project that is based at MSU. I also wanted to post this because the overarching problem of enacting high-level mathematical tasks is identical to the problem I view myself addressing with my practicum and dissertation. Thus, my individual work may be informed by (and possibly inform a small piece of) the work that comes out of this conference.
Personal Direction (Level: middle school)
As was discussed, it is remarkably difficult to establish and maintain cognitive demand within mathematical tasks. Past work has examined how the setup of the task plays a role as well as how the cognitive demand can decrease throughout the enactment. For my practicum, I want to look closely at "task conclusions" to see whether the way the task is characterized there aligns or misaligns with the enacted task (e.g., the conclusions emphasizes correct answers whereas mathematical processes were emphasized during the task proper) and aligns or misaligns with the teacher's intention for the task. Then, for my dissertation, my thought at this point is that I will examine the relationship between post-task phases (i.e., task conclusions and assessments) and student outcomes. This work is based on two related assumptions: (1) that tasks are foundational blocks of mathematics instruction, and (2) tasks cumulatively have an effect on two student outcomes -- achievement and conceptions of mathematics. (I personally believe that the latter student outcome is just as important as the former.) It is through tasks that students form an idea of what it means to learn and do mathematics, and I am interested in learning more about what contributes to these ideas, specifically the post-task phases which have the "last word."
In the framework above, I see this work falling directly on the arrow between "Enacted Curriculum" and "Student Learning," bringing in some pieces of the "Explanations" (i.e., teacher beliefs).
Bob Floden
Level of involvement
I would be interested in being involved as an advisor and occasional contributor.
Other proposals that may be relevant
Alan Schoenfeld and I just submitted a proposal to the REESE competition that fits toward the right hand side of the diagram. If funded, we will be studying pedagogical practices that affect what middle school pupils are doing to solve algebra word problems. We'll be making the link to pupil learning. We will plan to situate the work in settings where teachers are using curricula that promote student-student discussion, build socio-mathematical norms, and push for deep engagement in the mathematics. I'll paste the Summary from the proposal below.
Collaborative Research: Classroom Practices that Lead to Student Proficiency with Word Problems in Algebra
Alan Schoenfeld (UC Berkeley) and Robert E. Floden (Michigan State University)
This proposal addresses REESE Program Solicitation NSF 08-585, (A) Research on Emerging Topics in STEM Education, (2) Cognitive processes underlying STEM learning and teaching. We propose a three-year exploratory study focusing on the detailed description and analysis of mathematics classroom practices that result in students’ development of proficiency in word problems in algebra. The products of this research will be (a) an enhanced understanding of the mechanisms of “teaching for mathematical proficiency” in a centrally important area of the mathematics curriculum, (b) a set of research tools that supports deeper investigation into the mechanisms of teaching for robust mathematics learning, and (c) a set of practical tools that can be used on a large scale for benchmarking and improving teaching practice.
A fundamental goal of mathematics education is to prepare students to be flexible and resourceful learners and users of mathematics. As indicated by Adding it up (NRC, 2001), the goal of mathematics instruction – mathematical proficiency – includes conceptual understanding, procedural fluency, strategic competence, adaptive reasoning, and productive disposition. The key question addressed in this proposal is, How is such proficiency brought to life in highly effective mathematics classrooms? Given the national emphasis on “Algebra for All” (NCTM, 2000; National Mathematics panel, 2008) and the pivotal role of algebra in school mathematics and in shaping students’ mathematical futures, we focus on algebra classrooms. We focus on word problems because they are central to the curriculum and to students’ success, and because fluency in solving algebra word problems demands a wide range of mathematical sense-making, modeling, representational and procedural skills. We concentrate attention on teachers whose pedagogical practices emphasize student autonomous engagement with mathematical content.
Specifically, we propose to explore the following two questions: (1) What instructional practices are frequently used by teachers judged to be doing an exceptional job of helping students to develop proficiency in solving word problems? and (2) What analytic procedures can be developed and used to characterize these promising teaching practices, with low enough cost so that connections between teaching and learning can be examined for a large number of classrooms?
We will examine the instructional practices of carefully selected master teachers, seeking to identify practices that result in powerful student learning. In year 1 we will solicit and examine the videotapes of a range of teachers selected for demonstrated success in helping a wide range of students perform well in mathematics. We will use multiple analyses, at varied levels of grain size – from the establishment of classroom norms (e.g., Horn, 2008; Yackel & Cobb, 1996) to the detailed study of turn-by-turn classroom exchanges (e.g., Schoenfeld, 1998, 2002) and student interviews (Ball & Peoples, 2007) – to identify mathematically productive classroom practices and related student understandings. The product of this research will be a series of tentative coding and analytic schemes. These will be refined in year 2, when we conduct analyses of teaching and student learning in a range of classrooms, seeking to link instructional practices with student outcomes. Year 3 will extend the study to larger n, codifying the results and producing analytic tools that can be used by the research community and by practitioners.
Intellectual Merit: The proposal will provide insights into the ways in which effective teachers promote mathematical proficiency in their students, and it will provide tools that will advance research into this complex and under-researched area. It promises a sharper characterization of the classroom dynamics that promote student proficiency in mathematics, and an unpacking of the relationships between such practices and student learning.
Broader impact: The project investigates one of the most problematic and important curricular areas in middle school and secondary mathematics, word problems in algebra. Given the current high-stakes testing regimes across the nation, many students’ academic fates literally depend on their success in algebra. Insights and widely usable tools that would help teachers and students do better in this centrally important area, and in mathematics teaching more generally, are desperately needed. The project has the potential to contribute to improved mathematics teaching and professional development in general, and to the improved teaching of algebra in particular.
Use the "Edit This Page" button and place your brief description of how you see yourself excitedly moving forward.
More specifically:
Glenda Lappan
In a specific area of mathematics (rational numbers or algebra), what happens to the mathematics as it is transformed through the four stages of the framework?
Sandra Crespo
I like Glenda's question at the preservice setting;
what happens to a particular math idea as it moves through the sequence of written, enacted, and learned curriculum inside a teacher preparation program --- within math content courses and within math methods courses.
Sandra Crespo
(again)
I am currently working on my CAREER project that I see has connections to this group
1. Study of preservice teachers' development of practices of posing, interpreting, and responding
As part of this study we have looked at the opportunities to learn that pteachers in MSU program have had to learn these three practices in the math for teaching and math methods courses. We have looked at the written curriculum for clues into what about these practices one might expect preservice teachers to learn in our program.
As part of this collective --- I can imagine a project that does a more fine grained analysis of opportunities to learn of a particular math idea and practice (say algebraic thinking and how to pose tasks within that strand).
Jeffrey Choppin
Level of involvement
For the next 2 years, I cannot commit substantial time to any new projects. I am just beginning a 5-year CAREER grant (described in more detail below) and am 2 years from submitting my tenure package, so I will need to spend most of my time in the immediate future writing from my current study.
Description of CAREER grant - Adapting Curriculum for Learning in Mathematics Education (ACCLIME)
I will describe the ways my CAREER grant fits into the framework put forth by the group today. The CAREER grant focuses on mostly experienced CMP teachers who have received considerable CMP-specific professional development and who teach in districts that have used CMP as the primary curriculum resource for 5 or more years.
The study focuses on teacher knowledge of the ways that CMP units engage students with mathematical content. I use a unit as the level of analysis in order to get at teachers’ understanding of how ideas develop over the unit. For a subset of teachers, I have longitudinal data that look at successive enactments of the same unit over 2 or 3 years to see how their adaptations reflect teacher knowledge of student thinking and teacher learning with respect to how the CMP materials engage students. I have also studied the policy context around the adoption and implementation of CMP to provide background for the ways that the teachers use CMP.
The ways that I see that my study contributing to the set of studies is that it looks at teacher learning through enacting curricula. I can also connect teacher learning, and curricular orientations, to teachers’ practices that contribute to maintaining cognitive complexity, which I characterize as teaching for understanding. My data and analysis can speak directly to the framework, though with the major limitation that I do not focus on student learning.
Jon Davis
My Interest
I am interested in the maintenance of high cognitive demand of tasks across the written, intended, and enacted curriculum and its connection to student learning. If I was to zoom in on one component of that slice it would be the implementation of high cognitive demand tasks in the enacted curriculum and the roles that the curriculum plays in preparing high school mathematics teachers for that enactment in addition to the learning that may or may not occur by teachers in this area as they enact these tasks.
My Role
I am interested in being a co-PI on a project and working on the proposal. While I won’t be there physically to write the proposal as part of a group I am interested in contributing from a distance by taking turns developing a draft.
Recent Proposal
I recently submitted an NSF REESE proposal with Jeff Shih at the University of Nevada – Las Vegas and Rich Brown at USC. The intent of that proposal is to develop valid and reliable measures of specialized content knowledge (SCK), knowledge of content and students (KCS), and knowledge of content and teachers (KCT) in introductory high school algebra. We also intend to gather large-scale information on how teachers read, evaluate and adapt three NSF-funded and three commercially developed high school curricula as well as the nature of the enacted curriculum within these different programs. During year three of the project we are looking for connections between teachers’ use of curricular resources, the enacted curriculum, and growth in SCK, KCS, and KCT.
Kristen Bieda
I am interested in devoting a significant chunk of time to a project related to this work, in a co-PI capacity.
I would like to propose a study around the question of: In what ways are teachers' conceptions of the coherency among "big ideas" or concepts in a unit or a succession of units influenced by the curriculum in its various stages of implementation? I am particularly interested what happens with teachers' conceptions of the coherency as the lesson or unit is enacted. This study fits into the framework proposed by the group as the purposes of engaging students in cognitively demanding tasks is only relevant for teachers if they recognize how the content is part of a bigger, coherent "whole." Additionally, teachers' ability to situate content from a task to the mathematical goals for a unit is a part of mathematical knowledge for teaching.
I am also interested in examining mentor/intern interactions around K-12 curriculum. While PSTs' experiences in methods courses may support their emerging practices in enacting tasks from the K-12 curriculum at a high level, their mentor teachers may or may not "sanction" (for lack of a better word) these practices. Another way of studying these interactions would be to look at how mentor teachers' and PSTs' conceptions of the mathematics in the curriculum evolve during these interactions.
Janine Remillard
My Interests
I find all of components of the research framework interesting, however, with respect to what I would like to actually take on, I can imagine two, related areas of work. First, I am interesting in analyzing curriculum materials with an eye toward developing clearer and more precise ways of describing and categorizing them. I am particularly interested in developing a set of dimensions of curriculum materials that might be used classify them (that move us beyond categories like reform and traditional). Some of these dimensions (as described in others’ research) fit into the broad categories of a) mathematical stance (underlying assumptions about what it means to learn mathematics, how the content is organized, nature of tasks or cognitive demand), b) pedagogical stance, including the uses of formative assessments c) support for teacher use (how the resource communicates with the teacher). Second, I am interested in examining how teachers interact with the materials—specifically the components described above. I’m curious about how and what teachers read, the process by which the “intended curriculum” is designed, and the various factors (individual, contextual, curricular) that influence it.
Level of Involvement
I imagine myself being substantially involved in both these lines of inquiry as a PI/CoPI or as one of the senior personnel. This includes working on the proposal.
Other Research on the Burner
I am currently working on a proposal with Ok-Kyeong Kim at WMU that will be submitted to DRK-12 in January. This study is an exploratory study seeking to conceptualize and develop instruments to measure pedagogical design capacity. If funded, the project would involve three years of work.
Mary Kay Stein
Level of Involvement
I am interested in being involved at the level of PI/Co-PI.
Ideas for a Study
I would be most interested in designing a study that examines how context (school/district characteristics and interaction patterns) and curricular features shape teacher learning. I could imagine being paired with someone who is undertaking a close-up examination of curricular materials and how teachers use them; I could design a complementary focus on how those same teachers interact with others (peers, coaches, principals) around the curriculum and to what end. Resources permitting, it would be useful to also trace the between-community boundary practices that shape and are shaped by the curriculum.
Prior Related Work
I had an IERI grant that examined the scale up Everyday Mathematics and Investigations in two districts.
Michelle Cirillo
Corey Drake and I have been working on expanding her ideas about curriculum vision (first addressed by Drake & Sherin in Remillard, Herbel-Eisenmann, & Lloyd (in press)). Corey, Beth, and I wrote a series of questions designed to
help teachers develop and then enact their curriculum vision. These questions explicitly ask teachers to consider factors that influence their curriculum enactment such as national and state standards, their beliefs about the
balance of procedural fluency and conceptual understanding, the curriculum vision of their curriculum materials, and so forth.
We are interested in testing out the hypothesis that asking a teacher to explicitly think about and use his/her curriculum vision would have a positive impact on student learning. Corey and I are interested in being co-PIs (with others invited to join) on this work. We would be interested in testing this idea out in PD (and follow-up) with teachers who are enacting a new set of curriculum materials next fall (one site already identified) as well as in
districts that have already been using their materials.
We see this as fitting into the framework through comparisons of enacted
curriculum (where the written curriculum is constant for participating
teachers). We could see investigating this transformation through a particular
content focus, such as rational number.
Raven McCrory
For the last 3 years, I have been doing a study of undergraduate classes for elementary teachers. The study, called ME.ET (the Mathematical Education of Elementary Teachers) has aimed to understand what mathematics is being taught, by whom, with what resources, and with what results. We have a lot of data and are now analyzing it, with some interesting outcomes. For more information about the project, see the Web site, http://meet.educ.msu.edu.
Ideas for Studies
Hypotheses:
ADD: attention to and use of K-12 curricula
Nesrin Cengiz
My Interest
I am interested in the implementation of high-level tasks in grades K-8.
Particularly, I'd like to explore the relationship between the support provided
in the teacher guide materials and the ways in which teachers maintain the
cognitive demand of the high-level tasks during curriculum enactment. Some of
the questions that I have in mind are:
- What is the nature of the support provided in the curriculum materials to
specifically help teachers maintain the level of the cognitive demand of thetasks during curriculum enactment?
- How do teachers read and interpret that kind of information? How do they
use that kind of information during the implementation of the tasks?- What is the knowledge that teachers need to have in order to be able
read, interpret, and use the support provided in the curriculum materials in away that allows them to maintain the cognitive level of the tasks?
Level of Involvement
I am certainly interested in being involved in writing a proposal. As a junior
faculty, though, I feel like I need to know more about possible options for the
level of involvement.
Jill Newton
Involvement: I would be interested in collaborating on a grant with faculty
interested in similar/related research questions.
Possible questions of interest:
• In what ways are curricula (K-12 curriculum materials) being used in
teacher education programs? What is the payoff for these practices?
• What are the components (curriculum?) of current secondary mathematics
methods courses? What is the overall structure of secondary mathematics
teacher education programs (What courses? In what sequence? What field
experiences?)?
• How can/do inservice teachers implement standards-based practices/tasks in
schools where a more traditional text has been adopted?
Sarah Sword
I'm wondering about what it means for a teacher to have a robust enough
understanding of the mathematics of a particular curriculum to be able to make
informed decisions about implementation - how to use student (and teacher
support) materials effectively, even as the context around the teacher (and the
curriculum) varies.
Sharon Senk
I have been working on several projects in recent years that have developed
instruments to assess knowledge for teaching mathematics. The samples include
local MSU students as well as international samples. In a new study, I would
like to use these instruments (and modifications of them and others that might
be available) to investigate the nature and growth of knowledge for teaching
mathematics and factors that contribute it. Specifically, I would like to study
the following:
1. additional work on construct and instrument development
2. effects of mathematics courses for future elementary teachers and methods
courses on knowledge for teaching mathematics
Ideally, I would like to make this a longitudinal study that follows a group
from several universities into the first few years of teaching.
I am also very interested an experienced in fine grained analysis of
curriculum, especially algebra, geometry, reasoning and proof in K-16
mathematics.
Jack Smith
Level of involvement
I am fully booked on a current project and therefore have been cautious to do more with ExCITE than to help support the directions set by others. I cannot be directly involved, though I am interested in seeing the proposal that emerges and to see where there are connections to and potential synergies my current work (see below).
My take or slice of the proposed direction
In general, I am interested in the nature and dynamics of enactments of written curricula, of all types-especially for problematic content like fractions/rational numbers, algebra, and measurement.
Current proposed projects
The project that I just sent to NSF-REESE is a continuation of the my current STEM project which is examining the spatial measurement (length, area, and volume) content of three elementary mathematics curricula (as written)-Everyday Mathematics, Scott-Foresman/Addison-Wesley's Mathematics, and Saxon Mathematics-for their capacity to support robust student learning. In particular, we are looking for and coding each and every element of conceptual, procedural, and conventional knowledge related to measurement in each curricula. The objective is very detailed (and different sort of) opportunity to learn analysis. (We initially proposed carrying this examination through the middle grades (6-8) but the work on the elementary programs has been slower than I expected; we have not gotten to middle school yet.)
The proposed project will complete the analysis of written curricula; carry out discussions with the curriculum authors in the hopes that we can make our sense of important deficits clear and compelling (all have indicated interest in meeting with us); develop PD/summer institutes for practicing teachers and a "unit" in the mathematics methods course here at MSU for pre-service teachers that focus on (a) measurement lessons in written curricula, and (b) key conceptual content like unit iteration; and finally initiate a 'measurement mini-Center" of the major national research teams that will meet regularly to discuss and integrate their findings to get more "bang" for the national (mostly NSF) buck.
Sam Otten (just a grad student)
Level of involvement
I would be interested in serving as a graduate assistant for a project that is based at MSU. I also wanted to post this because the overarching problem of enacting high-level mathematical tasks is identical to the problem I view myself addressing with my practicum and dissertation. Thus, my individual work may be informed by (and possibly inform a small piece of) the work that comes out of this conference.
Personal Direction (Level: middle school)
As was discussed, it is remarkably difficult to establish and maintain cognitive demand within mathematical tasks. Past work has examined how the setup of the task plays a role as well as how the cognitive demand can decrease throughout the enactment. For my practicum, I want to look closely at "task conclusions" to see whether the way the task is characterized there aligns or misaligns with the enacted task (e.g., the conclusions emphasizes correct answers whereas mathematical processes were emphasized during the task proper) and aligns or misaligns with the teacher's intention for the task. Then, for my dissertation, my thought at this point is that I will examine the relationship between post-task phases (i.e., task conclusions and assessments) and student outcomes. This work is based on two related assumptions: (1) that tasks are foundational blocks of mathematics instruction, and (2) tasks cumulatively have an effect on two student outcomes -- achievement and conceptions of mathematics. (I personally believe that the latter student outcome is just as important as the former.) It is through tasks that students form an idea of what it means to learn and do mathematics, and I am interested in learning more about what contributes to these ideas, specifically the post-task phases which have the "last word."
In the framework above, I see this work falling directly on the arrow between "Enacted Curriculum" and "Student Learning," bringing in some pieces of the "Explanations" (i.e., teacher beliefs).
Bob Floden
Level of involvement
I would be interested in being involved as an advisor and occasional contributor.
Other proposals that may be relevant
Alan Schoenfeld and I just submitted a proposal to the REESE competition that fits toward the right hand side of the diagram. If funded, we will be studying pedagogical practices that affect what middle school pupils are doing to solve algebra word problems. We'll be making the link to pupil learning. We will plan to situate the work in settings where teachers are using curricula that promote student-student discussion, build socio-mathematical norms, and push for deep engagement in the mathematics. I'll paste the Summary from the proposal below.
Collaborative Research: Classroom Practices that Lead to Student Proficiency with Word Problems in Algebra
Alan Schoenfeld (UC Berkeley) and Robert E. Floden (Michigan State University)
This proposal addresses REESE Program Solicitation NSF 08-585, (A) Research on Emerging Topics in STEM Education, (2) Cognitive processes underlying STEM learning and teaching. We propose a three-year exploratory study focusing on the detailed description and analysis of mathematics classroom practices that result in students’ development of proficiency in word problems in algebra. The products of this research will be (a) an enhanced understanding of the mechanisms of “teaching for mathematical proficiency” in a centrally important area of the mathematics curriculum, (b) a set of research tools that supports deeper investigation into the mechanisms of teaching for robust mathematics learning, and (c) a set of practical tools that can be used on a large scale for benchmarking and improving teaching practice.
A fundamental goal of mathematics education is to prepare students to be flexible and resourceful learners and users of mathematics. As indicated by Adding it up (NRC, 2001), the goal of mathematics instruction – mathematical proficiency – includes conceptual understanding, procedural fluency, strategic competence, adaptive reasoning, and productive disposition. The key question addressed in this proposal is, How is such proficiency brought to life in highly effective mathematics classrooms? Given the national emphasis on “Algebra for All” (NCTM, 2000; National Mathematics panel, 2008) and the pivotal role of algebra in school mathematics and in shaping students’ mathematical futures, we focus on algebra classrooms. We focus on word problems because they are central to the curriculum and to students’ success, and because fluency in solving algebra word problems demands a wide range of mathematical sense-making, modeling, representational and procedural skills. We concentrate attention on teachers whose pedagogical practices emphasize student autonomous engagement with mathematical content.
Specifically, we propose to explore the following two questions: (1) What instructional practices are frequently used by teachers judged to be doing an exceptional job of helping students to develop proficiency in solving word problems? and (2) What analytic procedures can be developed and used to characterize these promising teaching practices, with low enough cost so that connections between teaching and learning can be examined for a large number of classrooms?
We will examine the instructional practices of carefully selected master teachers, seeking to identify practices that result in powerful student learning. In year 1 we will solicit and examine the videotapes of a range of teachers selected for demonstrated success in helping a wide range of students perform well in mathematics. We will use multiple analyses, at varied levels of grain size – from the establishment of classroom norms (e.g., Horn, 2008; Yackel & Cobb, 1996) to the detailed study of turn-by-turn classroom exchanges (e.g., Schoenfeld, 1998, 2002) and student interviews (Ball & Peoples, 2007) – to identify mathematically productive classroom practices and related student understandings. The product of this research will be a series of tentative coding and analytic schemes. These will be refined in year 2, when we conduct analyses of teaching and student learning in a range of classrooms, seeking to link instructional practices with student outcomes. Year 3 will extend the study to larger n, codifying the results and producing analytic tools that can be used by the research community and by practitioners.
Intellectual Merit: The proposal will provide insights into the ways in which effective teachers promote mathematical proficiency in their students, and it will provide tools that will advance research into this complex and under-researched area. It promises a sharper characterization of the classroom dynamics that promote student proficiency in mathematics, and an unpacking of the relationships between such practices and student learning.
Broader impact: The project investigates one of the most problematic and important curricular areas in middle school and secondary mathematics, word problems in algebra. Given the current high-stakes testing regimes across the nation, many students’ academic fates literally depend on their success in algebra. Insights and widely usable tools that would help teachers and students do better in this centrally important area, and in mathematics teaching more generally, are desperately needed. The project has the potential to contribute to improved mathematics teaching and professional development in general, and to the improved teaching of algebra in particular.